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Proof step 10 from proof nodups (previous step)

∀ a. a ∈ x ↔ a ∈ y ⊦ dups(y), dups(x), y ⊆m x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y))
Proof step 12:
∀ a. a ∈ x ↔ a ∈ y ⊦ dups(x), dups(y), ∀ a. #oc(a, y) ≤ #oc(a, x)

Rule argument

spec: <toplevel> name: msubset seq: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y)) subst: [y, x] → [x, y] flags: <all paths>

Additional information

Used terms: x, y